If you manually reset the board does the LED "breathe" for several seconds? Once it stops breathing does it start blinking with a period of two seconds?

No.

On this part specifically, does the LED "breathe" after a manual reset?

And, fter a few seconds of breathing does it start blinking with a period of two seconds?

In normal operation those are two distinct phases. Breathing indicates that the bootloader is running. After the bootloader runs for a few seconds it starts the sketch. On a fresh board you should see blinking because they load the Blink sketch at the factory to test. Of course, if you've managed to upload any sketch it will overwrite Blink but it doesn't sound like you've ever had success?

Also, can you confirm that Device Manager shows the board enumerated and drivers loaded in both bootloader and sketch mode? Just open Device Manager, check that you have an entry for the Leonardo without any errors or warnings (sketch mode), then manually reset the board and confirm that it comes up again with no errors or warnings (bootloader mode). Eventually it should automatically reset and go back into sketch mode. If you want to confirm which you're seeing, look at the PIDs: 0x0034 is bootloader, 0x8034 is sketch.